Using 91-octane premium fuel instead of 87-octane regular fuel will only increase your engine's power if your car's manufacturer specifically designed the engine to require it.
Higher octane fuel resists knocking or 'pinging' under compression, which is a premature ignition of the fuel-air mixture. Engines designed for higher octane can take advantage of this resistance to operate at higher compression ratios or with more advanced timing, which can lead to increased horsepower and efficiency. However, if your vehicle's owner's manual specifies regular 87-octane fuel, using premium 91-octane will likely offer no discernible performance benefit and is generally not recommended. Always consult your vehicle's manual for the correct fuel grade.
Fuel octane requirements are determined by the vehicle manufacturer and using a higher octane than recommended typically provides no benefit.
How can I determine if premium gas is necessary for my driving style?
Your driving style alone doesn't determine the necessity of premium gas; the vehicle's engine design is the deciding factor. If your car's owner's manual specifies premium fuel, then it is necessary regardless of how you drive. Engines designed for premium fuel can utilize its higher octane to perform more efficiently and powerfully under various conditions, including aggressive acceleration. If your car is designed for regular fuel, your driving style won't magically make premium fuel beneficial. Using premium in a car not designed for it will simply result in higher fuel costs without any performance gain.